The Lensmaker's Equation: Focal Length from Curvature

1 · Predict

A lens's focal length comes from its glass index and the curvature of its two surfaces. Does making one surface flatter (larger radius of curvature) increase or decrease the focal length?

• Increases — a flatter surface (larger radius) bends light less strongly, giving a longer focal length.
• A flatter surface decreases the focal length.
• Surface curvature doesn't affect focal length, only the glass index does.

2 · Set Up

1. Open the lensmaker preset and press Reset. This lens has index n = 1.5, with its second surface radius fixed at R₂ = −20 cm.
2. Enable the focal-length readout.
3. Set the first surface's radius of curvature for each trial and record the resulting focal length.

3 · Collect Data

Plot focal length f (y-axis) against R₁ (x-axis) for your three trials.

4 · Analyze

1. For one trial, compute f from 1/f = (n−1)(1/R₁ − 1/R₂) using n = 1.5, R₂ = −20 cm. Compare to the table.
2. Explain, using the lensmaker's equation, why increasing R₁ (making the first surface flatter/less curved) increases the focal length — a flatter lens bends light less.

5 · Extend

1. This lens has R₁ > 0 and R₂ < 0 — both surfaces bulge outward (a biconvex lens), the strongest common converging shape. Explain, using the lensmaker's equation, why a plano-convex lens (one flat side, R = ∞) has a longer focal length than a biconvex lens of the same glass and comparable curvature.
2. Eyeglass lens manufacturers choose surface curvatures (not just glass index) to achieve a prescribed focal length while controlling weight and edge thickness. Explain why two different (R₁, R₂) pairs could give the exact same focal length, using the lensmaker's equation's structure.

The Physics Behind This Experiment

← Back to experiment